Charlotte's Web is the first book I can remember reading myself. At least, I tried to read it. I can still vividly picture myself at age 6 on the top bunk at summer camp going through the book. I know I didn't know what all of the words were then, but what I do know is that I loved that book.
NPR just did a great feature on it, and you can read the article here.
What was your favorite book when you were young? Or better yet, do you remember the first book you read by yourself?